Geodesic
New extension of the variational McShane integral of vector-valued functions
Mathematica Bohemica, Tome 144 (2019) no. 2, pp. 137-148

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset $G$ of $m$-dimensional Euclidean space $\mathbb {R}^{m}$. It is a "natural" extension of the variational McShane integral (the strong McShane integral) from $m$-dimensional closed non-degenerate intervals to open and bounded subsets of $\mathbb {R}^{m}$. We will show a theorem that characterizes the Hake-variational McShane integral in terms of the variational McShane integral. This theorem reduces the study of our integral to the study of the variational McShane integral. As an application, a full descriptive characterization of the Hake-variational McShane integral is presented in terms of the cubic derivative.
DOI : 10.21136/MB.2018.0114-17
Classification : 28B05, 46B25, 46G10
Keywords: Hake-variational McShane integral; variational McShane integral; Banach space; $m$-dimensional Euclidean space 
@article{10_21136_MB_2018_0114_17,
     author = {Kaliaj, Sokol Bush},
     title = {New extension of the variational {McShane} integral of vector-valued functions},
     journal = {Mathematica Bohemica},
     pages = {137--148},
     publisher = {mathdoc},
     volume = {144},
     number = {2},
     year = {2019},
     doi = {10.21136/MB.2018.0114-17},
     mrnumber = {3974183},
     zbl = {07088841},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0114-17/}
}
TY  - JOUR
AU  - Kaliaj, Sokol Bush
TI  - New extension of the variational McShane integral of vector-valued functions
JO  - Mathematica Bohemica
PY  - 2019
SP  - 137
EP  - 148
VL  - 144
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0114-17/
DO  - 10.21136/MB.2018.0114-17
LA  - en
ID  - 10_21136_MB_2018_0114_17
ER  - 
%0 Journal Article
%A Kaliaj, Sokol Bush
%T New extension of the variational McShane integral of vector-valued functions
%J Mathematica Bohemica
%D 2019
%P 137-148
%V 144
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0114-17/
%R 10.21136/MB.2018.0114-17
%G en
%F 10_21136_MB_2018_0114_17
Kaliaj, Sokol Bush. New extension of the variational McShane integral of vector-valued functions. Mathematica Bohemica, Tome 144 (2019) no. 2, pp. 137-148. doi: 10.21136/MB.2018.0114-17

Cité par Sources :